The generator matrix

 1  0  1  1  1  1  1  X  1 2X  1  1  1  1  1 2X X^2  1  1  1 X^2+X  1  1  1  1  1  1 2X X^2  1  1  1  1 2X  1  1 2X^2+2X  1  1  1 2X^2+X  1  1  1  1  X  1  1  1 X^2+2X  X  1  1  1 2X^2+2X  1  X  1 X^2+X  1  1 2X^2+2X  1  1  1  1  1  1  1  1  1  1 X^2+X  1 2X^2+2X  X  1  1  1  1  1  1 X^2+2X X^2+2X  1  1  1  1  1 X^2+X  1  1  1  1  1 2X^2
 0  1  1  2 2X^2 2X+1  2  1  2  1  0 2X^2+2X+1 2X^2+2X+1 2X^2 X+2  1  1 X+1  0 2X^2+X+2  1  0  1 2X^2+2X+2 X^2 X+1 2X^2+2X+2  1  1 2X^2+2 2X 2X^2+2X+1 2X+2  1 2X^2 2X^2+2X+1  1 X^2+2X+2 X^2+X+1 2X^2+2X  1 2X^2 X^2+2X+2 X^2+2X  2  1 X^2+2X+1 2X^2+2X+2  X  1  1 2X^2+X X^2+2X+1 2X^2+2X+1  1 X^2+2  1 X+2  1 2X^2+2 X^2+2X+2  1 X^2+X+1  X X+1 X^2+X X^2+X  1 X^2+2X+2 2X+2 2X^2+2X+1 X^2+2X  1 X+1  1  1 X^2+2X+1 X^2+X X+2 X^2+2X+1 2X^2+X+1 X^2+X+2  1  1 X+2 2X 2X^2+X+1 2X^2+2  2  1 X^2+2 2X^2+X+1 X^2+2 X^2+X+2 2X^2+2  1
 0  0 2X  0 2X^2  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 2X^2+X 2X^2+X X^2+2X  X X^2+X X^2+2X X^2+2X X^2+X 2X^2+X X^2+2X  X 2X^2+2X 2X^2+X  X 2X^2+2X  X X^2+2X 2X^2+2X 2X 2X^2+2X 2X^2+2X X^2+X X^2+X X^2+2X 2X X^2 2X^2 X^2+2X 2X^2+2X  0 X^2+X X^2+2X X^2 X^2+X 2X^2 2X  X 2X^2+2X  0  X 2X^2+2X  X 2X 2X^2 2X 2X^2+2X 2X^2+X 2X^2 X^2+X X^2+2X 2X^2+X X^2+X 2X^2 2X^2+2X  0 2X^2+X  X  0 X^2+X 2X^2 2X  X 2X^2+2X 2X 2X^2+X 2X^2+2X 2X  0  0 2X^2+X 2X 2X^2+2X X^2+X X^2+X 2X^2 X^2+X 2X^2+X 2X^2+X X^2+2X 2X^2+X 2X^2+2X  X  0
 0  0  0  X 2X^2+X X^2+X X^2  X X^2+2X X^2+2X 2X  0 2X^2+2X 2X^2+2X X^2+2X X^2+2X 2X^2 X^2+2X  0 2X^2  X X^2 2X^2+X 2X^2 X^2+X 2X^2 2X^2+X X^2 2X X^2+X 2X^2+2X X^2+2X X^2+2X 2X^2+X 2X^2+X  X  0 2X^2+X 2X^2+X  X  0  0 2X^2+2X 2X^2+2X X^2+2X X^2+2X 2X^2 X^2+X 2X^2+2X 2X^2+2X 2X^2+2X X^2 X^2+2X X^2  0 X^2 2X^2 2X^2+X X^2+X 2X 2X^2 2X^2+X 2X^2+X  0 X^2+X X^2+2X  X 2X^2+2X 2X^2+X X^2+2X 2X^2 2X X^2+2X X^2 X^2+2X  X 2X^2+2X  X 2X^2  0 2X 2X^2+2X 2X^2 X^2 2X^2+X X^2  X  X 2X 2X^2+X 2X^2+X 2X^2+2X 2X^2  0 X^2+2X 2X

generates a code of length 96 over Z3[X]/(X^3) who´s minimum homogenous weight is 181.

Homogenous weight enumerator: w(x)=1x^0+300x^181+468x^182+740x^183+1242x^184+1944x^185+2510x^186+2724x^187+3204x^188+4460x^189+3516x^190+4608x^191+6480x^192+4560x^193+4728x^194+5706x^195+3390x^196+2736x^197+2262x^198+1152x^199+852x^200+366x^201+348x^202+228x^203+24x^204+96x^205+60x^206+12x^207+108x^208+84x^209+6x^210+24x^211+12x^212+22x^213+36x^214+12x^215+6x^216+18x^218+2x^219+2x^228

The gray image is a linear code over GF(3) with n=864, k=10 and d=543.
This code was found by Heurico 1.16 in 17.8 seconds.